Negative feedback amplifier circuit



Nov- 26, F. B. ANDERSON NEGATIVE FEEDBACK AMI'fLIFIER CIRCUIT Filed Aug. 5, 1939 2 Sheets-Sheet 1 lNl/E N TOR F. B. ANDERSON A 7' TORNE Nov. 26, i i F. B. ANDERSON NEGATIVE FEEDBACK AMPLIFIER CIRCUIT 2 Sheets-Sheet 2 b M 3 a D m F m H n M. .1." H X A u n M m w 0 0 mq -aot Emu 56 :53?

0 0 C k r m 2 M m M F r 0 2 w 2 mmlswu 3x o a a m m w FIG. 5

FIG. 4

FIG. 6

6b 10 dd d 00 w m w w u v R M INVENTOR I By F.5f. ANDERSON ATTORNEY Patented Nov. 26, 1940 PATENT OFFICE NEGATIVE FEEDBACK AIVIPLIFIER CIRCUIT Frithiof B. Anderson, Long Branch, N. .L, assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New ;York

Application August 5,1939, Serial m. 288,520 I I 4 Claims.

This invention relates to electron discharge device circuits and more particularly to a negative feedback'amplifier circuit of the general type disclosed in H. S. Black Patent 2,102,671, issued De- 5 cem-ber 21, 1937.

It has been observed'that when gain-reducing negative feedback amplifiers are operated with an amount of feedback less than infinite feedback or, from the practical standpoint, maximum feedback for the particular amplifier, that the amplifier gain over the operating band or range of the amplifier does not differ uniformly from the amplifier gain for the infinite feedback condition. Not only is there a non-uniform deviation over the frequency range, but as the departure in the amount of actual feedback below infinite feedback increases, the deviation increases and becomes more non-uniform with frequency over the frequency range. In the'case of an amplifier in a transmission line, having gain regulator means associated therewith for regulating the amplifier gain manually, or automatically, or both, with variations in transmission conditions, this means that for preassigned regulator settings for preassigned amounts of feedback or, conversely, am-

plifier gain, the expected amplifier gain down so many decibels from maximum gain for the amplifier over the operating band is not realized.

, This deviation effect has come to be referred to by those skilled in the art as the LB-effect.

It is an object of this invention to compensate or correct for this deviation effect so that the deviation, if any, for preassigned feedback level-s below infinite feedback will be constant over the operating frequency range of the amplifier.

In accordance with the invention, the feedback loop phase-frequency characteristic curve of the amplifier is modified at the sacrifice of some reduction in the possible maximum feedback loop 40 gain for the amplifier. This is done to satisfy the requirement that, if the deviations in amplifier gain at one frequency for two values of feedback loop gain, or MS], are to be in the same ratio as those at another frequency for two values of 43] of the same ratioas the first pair, the following relation should hold:

, e 1 lufili 11 611 cos 01] mm.

where M311 is equal to 1 6] at a frequency of f1; [#Blz, tol fll at a frequency 12; klll-Bll and k| 6l2,to 55' a constant times l pli and 512, respectively; (p1,

' to the phase angle of l lfili and kl pli; and (p2, to

the phase angle of Ipfllz and kllbplz. This relationmay be well approximated for [/Jfill cos (p1 and I fllz cos 2, of the order of 10 or more, by neglecting the last fractional ratio.

This gives:

A'more complete understanding of the invention will be obtained from the detailed descriptionwhich follows, taken in conjunction with the appended drawings, wherein:

Fig. '1 shows the circuit of a negative feedback amplifier;

Fig. 2"shows, inthe solid lines, typical ir-gain versus frequency and pit-phase versus frequency curves for the amplifier of Fig. 1, and, in the broken line, the ip-phase versus frequency curve necessary, in accordance with the invention, to 20 compensate for ip-effect if such ,ufi-gaill versus frequency characteristic is to be obtained;

I Fig. 53 shows amplifier gain deviation versus frequency curvesfor different values of feedback below maximum feedback for the amplifier;

Figs. 5 and 5 show networks that, in accordance with the invention, might be substituted for the networks shown between points A--A and for the first interstage network, respectively, of the amplifier of ,Fig. 1; and

Fig. 6 shows amplifier gain deviationversus frequency curves corresponding to those of Fig. 3, but evidencing the effect of modifying the amplifier of Fig. 1 in accordance with the invention.

The wave transmission system'of Fig. 1 comprises a negative feedback amplifier generally similar to that of the copending application of F. B. Anderson et al., Serial No. 202,180, filed April 15, 1938, now Patent No. 2,170,046 Aug. 22, 1939, for Negative feedback amplifiers, and is adapted for use as a line amplifier for amplifying carrier frequency currents transmitted over a nineteen-gauge non-loaded cable circuitcomprising an incoming line H] and an outgoing 45 line H. I

The amplifier comprises a plurality of electron discharge devices I2, l3, M, for example, sup-' pressor grid type tubes, connected in cascade by interstage networks'l5, I6. These networks comprise impedance coupling networks including series capacitiesand shunt inductances and resistances. The amplifier further comprises an input transformer 11, an output transformer l8, a ne ative feedback'path or connection 19, and an 55 derson et a1. Patent 2,106,336, issued January 25, 1938, is also included in the feedback path. This output bridge 29. The bridge connects the plate a resistance R, and two and Z2 1.

The feedback through the path amplifier gain but gives great improvement in quality and stability and greatly reduces har---- monic distortion. It includes a flat gain control potentiometer 2| including a potentiometer re sistance 22 having taps 23, 24, 25. A condenser potentiometer of the type disclosed in F. B. An-

con'denser potentiometer comprises a flat gain control'condenser G0, a fiat gain regulator condenser GR, and two trimmer condensers TR and t1. The condenser GC serves to vary, under manual adjustment, the amount of feedback to adjust the fiat gain of the amplifier through a range of, for example, 10 decibels. The condenser GR may be automatically operated, for example, by a pilot wire; gain regulator system 26 such as that" disclosed in F. A.

. Brooks Patent 2,075,775, issued April c, 1937, for

varying the amount of feedback, for example, over a range of 14 decibels, to compensate for the fiat portion of the variationsin the line loss with line temperature. I v

The potentiometer 2| also comprises a condenserzl, an inductance 28, and a blocking condenser 29. The condenser 21 and inductance 28 improve the high frequency phase margin of the amplifier against singing, for potentiometer settings on taps 23 and 24, and inductance 28 improves the high frequency margin for tap settin .25. The tapped resistance 22'supplies uniform losses over the 12-60 kilocycle band in the feedback loop, the capacity 21 and inductance 28 havin little effect in that frequency range; capacity 21 contributes phase margin at high frequencies above that range, and inductance 28in the shunt arm of the potentiometer neutralizes some of the capacity bridging this arm and further improves the phase shift. 1

. The-amplifier is coupled to the incoming line I0 through the transformer I1, and to the outgoing line I through the transformer l8. The condensers 30 and condenser 4| in the line windings of the transformers serve to make the amplifier impedances more nearly match the cable impedance and to make the line circuits of the amplifier open circuit to direct current used, for example, for cable tests. The condensers, moreover, contribute loss for frequencies below the 12-60 kilocycle band, to facilitate meeting the requirement that the amplifier gainbe considerably lessthan the cable attenuation'at these low frequencies 'forall gain settings of the amplifier. Condensers 30, having "equal capacities and their junction connected toground, also increase the longitudinal balance of the'system. A resistance 3|, having atap 32,- dividing it into two portions 33, 34 and each having a condenser 35 in shunt therewith, is connected across the secondary of The remaining four arms ,are consti-C tuted by the plate resistance Rp of the tube 14. inverse impedances Z 11 reduces the the input transformer. A movable contact 36 connected to the control grid of the discharge device |2 may be connected to tap 32 for reducing the fiat gain of the amplifier. These condensers 35 and the distributed capacity inherent in the secondary reduce any unfavorable high frequency phase shift that, especially with the contact 36 on the tap 32, the transformer l1 and its terminations introduce in transmission around the feedback loop, thus increasing the singing margin or the stability of the amplifier against self-oscillation at frequencies above the vserves tocompensate for the effect of the capacity to ground associated with terminal 37 so as to make the gain change due to a change in the setting of the GR condenser the same as it is with contact 36 on tap 31 and switch 38 open.

, Condensers 4|, 42, 43, 44 and 45 are blocking or by-pass condensers, each of negligible reactance in the pass band of the amplifier. 'Current .for the heaters of the tubes is supplied from battery 46, by-passed by condenser 41 for reducing crosstalk between amplifiers to which this battery maybe common. Plate and screen grid potentials for the tubes l2, l3 are supplied from battery 48 and a low-pass filter comprising choke 49 and condenser 50, through resistor 5| which serves to reduce cross-talk betweenamplifiers to which the battery may be common. Plate and screen potential for tube I4 is supplied by batteri'es 46 and 48 in series, the choke coil 52 in the cathode lead of tube |4 reducing alternating current flow through the battery. The cathode heating and space current supply system is of the general type disclosed in the copending application of J. O. Edson et al., Serial No. 82,156, filed May 27, 1936, now Patent No. 2,191,167 Feb. 20, 1940. Biasing potential for the control grid of tube I2 is obtained principally from the voltage drop across the network 53 in the cathode lead of that tube, this network comprisinga biasing resistor and a by-pass condenser-of 10wactance' in the 12-60 kilocycle band. A similar network 54 is provided in the cathode lead of the tube l3. With switches 55 and 56 in the positions shown in the drawings, biasing potential for the grid of tube I4 is obtained from voltage drop across the network 5'! and the coil 52, connected in series in the cathode lead of the tube l4. The network 5'! comprises a resistance shunted by a condenser of high reactan ce in the frequency range of the amplifier, the coil 52 being by-passed by the condenser 44, and the biasing potential is filtered by the resistance 58 and condenser43. If switch 56 should be closed so as to short-circuit the network5'l, the proper bias for the control grid of tube I4 is obtained by con-; meeting the switch 55 to its other contact to provide a grid biasing battery 59 in series with a resistance 69. Condenser 6| limits the impedance common to-the biasing circuits of several amplifiers such as the one shown and thus holds cross-talk, because of such coupling, it in assigned limits.

The network 62 in the cathode lead of tube l2 furnishes local negative feedback around the tube, for improving the singing margin of the amplifier, in accordance with D. D. Robertson Patent 1,994,486, issued March 19, 1935.

Network 54, which can be by-passedby a con denser 63 of negligible reactance in the trans mission band by closure of the switch, and the network-51, which "can be short-circuited by closure of switch 5.0; facilitate obtaining phase and gain conditions for transmission aroundlthe feedback loop-thatavoid singing for all adjustments of the movable-contact of the potentiometer N on the taps 23, 24, v2 5;: For a given setting of the condensersGC and'GR, the fiat gain of the amplifier is at its maximum value when the contact is on tap 23, with contact 36 on terminal 31 of the transformer Ill and the switches 56 and 64 closed. For a gain reduction from this maximum, the movable contactof potentiometer 2| is adjusted to tap ZA and" the switch 64 is opened.

For a furtherjgain reduction, the movable contact is ad'justed'totap 25 and the switch 56 is opened and switch 55 is asshown. A still further gain reduction is obtained by moving contact 36 to tap' 32 with switch 38 closed.

The output bridge should not only have suitable transmission and impedance properties in the operating band ofthe amplifier, but it should have favorable phase properties for the feedback loop above the band notwithstanding the high generator impedance of the tube M. In accordance with the disclosure of the copending application of Anderson et al., Serial No. 202,180, filed April, l5,' l9-38, with the constant resistance output bridge configuration, a satisfactory high frequency hase characteristic is obtained by associating with the load, including the output transformer l8 and the associated shunt capacities E5, 66, a network N to render the receiving impedance (i. e., the impedance of the bridge arm constituting. the load) a, substantially constant resistive impedance over not only the operating frequency band, but also a widefrequency range above thatband. In the drawing, that bridge arm is. designated K and the network N is shown connected in serial relation with the primary Winding of the transformer I8, between the plate of tube. ldcand the primary winding. The high impedance Rp of the tube I4 accentuates difficulties that the transformer and bridge constants contribute to stabilizing the feedback loop against oscillation at frequencies above the operating. frequency band. Such difiiculties, however, are overcome. by network N, which builds the transformer with its associated capacitances 65, (it out to a network K which has a constant resistance impedance.

InFig. 2, the solid line curves A and B aretypical maximum feedback or mS-gain versus. frequency and ip-phase versus frequency characteristic curves for an amplifier of the type described. Whether the amplifier operates at the condition of maximum feedback, i. e., maximum c-gain, isdetermined' by. the setting of the gain-regulating means in the feedback loop. It might be expected that, if the gain-regulating means in the feed-back loop is adjusted so that the amount of feedback is less than the maximum possible, at the reduced feedback thegain of the amplifier would be equally spaced or altered by the same amount from the gain at maximum feedback for all frequenciesin the operating band of the amplifier. This, however, is not the case. In Fig. 3. curves C, D, E show the deviation from the ideal or expected amplifier gain for feedback regulator settings for various amounts of feedback reduced below the maximum feedback. Of

course, in the ideal case of infinite feedback, therewould be no deviationwhatever. As a practical matter, however, the maximum feedback obtainable in the particular amplifier will not be infinite in value but finite Nevertheless, as Fig. 3 shows, the deviation will be the least for the condition of maximum feedback, and becomes more pronounced and more non-uniform with frequency as the actual feedback'is reduced more and more below the maximum. This effect has come to be designated by those working in the negative feedback amplifier field the pp-effect, and compensation or correction for this effect is an object of theinvention.

An explanation of thisso-called ip-effect is suggested V by the following analysis. In accordance with the mathematical treatment of negative feedback amplifiers in Black 2,102,671, let the electromotive force applied at the input to the amplifier be considered equal to e, and the potential actually effective on the control grid of the first stage because of the input e and the energy fed back from the output stage he considered equal to V. Then, if the amplification of the amplifier in its forward path is denominated ,u, and the fraction of the output fedback be denominated p,

If at is equal to infinity e becomes equal to Equation 4 shows that the factor I represents the deviation. from the ideal realized with infinite feedback (,u,B= The deviation factor is a complex quantity since 13 is a complex quantity, hence, the deviation factor should be written as 1 Ff/i It will be at a minimum and less than unity for (p=1r; a maximum and greater than unity for =0; and will approximate unity for go in the region of 1r/2 or 31r/2 for [;z;8| 1.

The analysis above suggests that if the deviation factor at the reduced value of feedback could be maintained constant over the operating band of the amplifier, there would be a constant, uniform deviation for each setting of the regulator means representing a particular feedback less than infinite feedback. This means that for deviations at one frequency for two values of p] to be in the same ratio as where ljtpli is equal to I e! at frequency 71 I 43] 2 is equal to-- lap} at frequency f2 (p1 is equal to the phase angle of l tfili 2 is-equal to the phase angleof filz which-may be reducedto :"'1 1m |1 ml/ fll1 cos c1 (7) M l 2 '1' r I 2 s c Since 1 Mt um. trait/rm. where k is a constant,

IMBhI w (9) ll flll l lnfilz c w l ZIP-BIZ 008 w This relation of Equation 7 may be approximated for p|1cos 1 and lpplcosr z, of the order of 10 or more by neglecting the last fractional ratio. This gives: v

Iufllf w p (10) This, of course, means that the B-gain or the ip-phase versus frequency characteristic of the amplifier, or both, must be modified. The 49- gain characteristic A, shown in Fig. 2, may be retained but the ,up-phase characteristic would have to be modified so as to follow curve B of Fig. ,2. It is simpler to modify both MB- ain and phase characteristics somewhat to correspond to Relation 10. One such pair of modified ip-phase and gain characteristics is obtainable for the amplifier of Fig. l by replacing the networks 53 and 62 by a network of the type shown in Fig. 4, and by replacing the interstage network 15 by that shown in Fig. 5, i. e., by such change in the network elements as will give the pl-phase and ip-gain characteristics that are in accord with the criteria developed herein.

The curves of Fig. 6 show that for the corresponding regulator settings for feedback 0, 110

and-'20 decibels below maximum feedback, the gain deviations over the operating range of the amplifier are constant.

What is claimed is: p

1. In an amplifying system, an amplifier, a circuit connecting the output and the input of said amplifier for feeding back output energy to said input insuch sense as to reduce the' gain of the amplifier, and means insaidfeedback circuit for regulating the magnitude of the feedback energy and thereby the magnitude of the amplifier gain, the feedback loop gain and the feedback loop phase versus frequency characteristics being such that for a given setting of the regulating means for a finite value of feedback the deviation from the preassigned gain-frequency characteristic of the amplifier for the given setting will be constant with frequency.

21A negative feedback amplifier in which the amplifier gain is equal to,

and in which p has some finite value, the feedback loop gain and the feedback loop phase versus frequency characteristics of the amplifier over the frequency range it is desired to amplify being such that, forfinite values of feedback loop gain, the expression I is substantially a constant.

3..Ihe method of adjusting for the p-efiect in a gain-reducing negative feedback amplifier tively, the deviations from the amplifier ideal gain at one frequency ii for two values lpfili and JCI ifili beingv inthe same ratio as those at the other frequency is for two values Ipfllz and kl tfilz of'the same ratio as the first pair, 70 being a constant.

4. The method of adjusting for the e-effect in a gain-reducing negative feedback amplifier having given maximum feedback loop gain and feedback loop phaseversus frequency characteristics, that comprises establishing the feedback gain and loop phase-frequency characteristics so that over the frequency band to be amplified they satisfy the approximate relation where bb and; l rfllz are the feedback loop gains at frequencies f1 and f2, respectively, and 1 and 2 are the phaseangles of lib/3h andlufilz, respectively, the deviations from, the amplifier ideal gainat one frequency ii for two values |m8|1 and kl/Lfill being in the same ratio as those at the other frequency f2 for two values l plzand kI/LfilZ of the same ratio'a's the first 'pair, is being a constant: g 1 Y I FRITHIOF B. ANDERSON. 

